The 30-year-old German lost control of his Mercedes when the right rear Pirelli tyre exploded at around 320 kph at the Blanchimont corner.
"That was definitely not fun," said Rosberg whose wife Vivian is expecting their first child at any time.
"I think a tyre broke at the rear, but I am not sure. Let's wait and see, but it was at the maximum speed on the lap. So that is not good.
The session was red flagged and suspended briefly while the car and debris were cleared from the spectacular and majestic, but challenging, circuit in the Ardennes forests.
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On resumption, Swede Marcus Ericsson lost control of his Sauber car and crashed heavily at the downhill Pouhon corner, a collision that produced the red flags again for a third time in the day.
Venezuelan Pastor Maldonado had set the pattern during opening practice in the morning when he hit the barriers at Malmedy. He also, like Ericsson, was unhurt.
In both of the afternoon accidents, the drivers were saved from more serious damage and possible injuries by the big run-off areas built into the circuit.
Hamilton was unable to improve his time and finished the session second fastest behind Rosberg, as he had been in the morning, when both the Red Bull and Ferrari teams produced improved speed to threaten the champion team's supremacy.
The incidents highlighted again the dangers that remain prevalent at one of the classic 'traditional' long and high speed F1 tracks where last year Hamilton and Rosberg's tense intra-team rivalry turned acrimonious and resulted in a collision during the race.